Rational number is one of the important contents in the field of number theory and algebra, and it is widely used in real life. It is the basis for continuing to learn real numbers, algebra, equations, inequalities, rectangular coordinate systems, functions, statistics and other mathematical contents and related disciplines. The following is a summary of the knowledge points in the first chapter of the seventh grade mathematics "Rational Numbers" which I carefully edited for you. Welcome to read!

I. Positive Numbers and Negative Numbers

1. In practice, the amount of opposite meaning rises by 5 meters, which is recorded as 5 meters; -8 meters means 8 meters down.

2. Positive number: a number greater than 0.

3. Negative number: add "-"before positive number.

The meaning of 4.0:

① neither positive nor negative;

20 means no counting, such as 0 yuan;

③0 represents a certain amount of reference, for example, 0℃ represents a temperature reference.

5. Classification of rational numbers

② the concept of score

(1) Primary school scores, percentages, finite decimals and infinite circulating decimals can all be converted into component numbers, which are now collectively referred to as fractions;

(2) Infinitely circulating decimals are not rational numbers, such as π = 3.141592 ... 2.01001 ....

③ The concept of "non-"

Non-negative number: positive number, 0 Non-positive number fraction: negative number fraction.

Non-positive: negative, 0 Non-negative: positive.

Non-negative integers: positive integers and 0.

Non-positive integers: negative integers and 0.

Second, the number axis

1. Three elements: origin, positive direction and unit length. Generally, the origin is represented by "O", the direction to the right is positive, and the unit length is 1.

2. How to draw a number axis

① Draw a straight line (generally horizontal), determine the origin and mark the origin "O";

② Take the direction of the origin to the right as the positive direction, and mark the arrow;

③ Select appropriate length as unit length, marked as -3, -2,-1, 1, 2, 3. ...

3. Points and rational numbers on the number axis:

(1) points on the number axis correspond to rational numbers one by one (2) the number on the left is 0 >; Negative number;

2. Comparison of two negative numbers

① The number represented by the point on the right is greater than that represented by the point on the left.

② The greater the absolute value, the smaller it is.

Third, the operation of rational numbers.

1. Addition of rational numbers:

General steps of adding:

① Determine symbols: the same symbols are used for the same numbers.

Symbols with large absolute values are symbols with addends.

② Determine the absolute value: add the absolute values with the same sign.

A symbol subtracts a smaller absolute value from a larger absolute value.

Two opposite numbers add up to 0. Add a number to 0 and you still get the number.

Additive commutative law with letters a+b=b+a; Additive associative law a+b+c=(a+b)+c=a+(b+c).

When three or more rational numbers are added together, it can be written as serial addition. For serial addition, according to addition,

The commutative law and the additive associative law can arbitrarily exchange the positions of addends or add a part first.

According to the characteristics of the formula, proper application of the algorithm can make the operation simple:

(1) Numbers with the same symbol are added first-the same symbol combination method.

(2) The first addition of reciprocal-the combination of reciprocal.

(3) Numbers with the same denominator are added first-a combination method with the same denominator.

(4) Positive numbers and positive numbers, decimal and decimal addition-isomorphic combination method.

2. Subtraction of rational numbers;

Law of subtraction: subtracting a number is equal to adding the reciprocal of this number.

Addition and subtraction are mixed operations, and subtraction is converted into addition and then calculated.

3. Algebraic sum: when rational numbers are mixed, the addition and subtraction are unified into addition operations, which are converted into the sum of several positive or negative numbers.

In the summation formula, the parentheses of each addend and the plus sign before the parentheses can be omitted and written as the sum of the omitted plus signs.

4. Rational number multiplication:

Multiplication step: 1. Determine the symbol: the same symbol means positive, and different symbols mean negative.

2. Absolute value: orthogonal.

Any number multiplied by 0 is 0. Multiply any number by-1 to get the reciprocal of that number.

Multiplication of multiple rational numbers:

When several nonzero rational numbers are multiplied, when the number of negative factors is even, the product is positive; When the number of negative factors is odd, the product is negative;

Multiplicative commutative law, multiplicative associative law and multiplicative distributive law;

5. Division of rational numbers:

Division step: 1. Determine the symbol: the same symbol is positive and different symbols are negative.

2. Absolute value: division.

Dividing by a number that is not equal to 0 is equal to multiplying the reciprocal of this number.

Divide 0 by any number that is not equal to 0 to get 0.

Fourth, the countdown.

① Two numbers whose product is 1 are called reciprocal.

② the reciprocal of a is 1(a≠0) of a.

③a and B are reciprocal ab= 1.

④ The reciprocal of a positive number is still positive, the reciprocal of a negative number is still negative, and 0 has no reciprocal.

Fifth, the multiplier

The operation of finding the product of several identical factors is called power.

a a … a=an

② Base, exponent and power